The value of the integral Ι = ∫ 0 π sin ⁡ x + cos ⁡ x d x , (where . denotes the greatest integer function) is equal to

Question

The value of the integral Ι = ∫ 0 π sin ⁡ x + cos ⁡ x d x , (where . denotes the greatest integer function) is equal to, 1, 2, π, 2 π

MARKS App · Accepted Answer

Let, y = sin ⁡ x + cos ⁡ x ⇒ y 2 = 1 + s i n 2 x ∈ 1,2 ⇒ y ∈ 1 , 2 ⇒ sin ⁡ x + cos ⁡ x = 1 Thus, Ι = ∫ 0 π 1 · d x = π - 0 = π